Doors and Windows - Door Confusion

Just placed a new pre-hung interior door into a 2x4" rough opening.

I am assuming the door is to be with an overhang of 1/2" width on both sides to make it accomodate the drywall to be flush to the sides of the frame.

However, if that is done, the striker plate opening sticks out enough to make fastening a screw marginal at best.

What am I doing wrong here.....Should the frame be set flush on the striker plate side and overhang the other?

This seems rather basic but after a lot of looking, there is a lot of advice about installing a door but nothing about how it is to be placed in the rough opening (even on both sides of the frame or flush on one side...

Thanks for any insight....

Correct: I am assuming the door is to be with an overhang of 1/2" [approx 3-5/8 + 1 = 4-5/8 Stand Jamb = 4-9/16 ] width on both sides to make it accomodate the drywall to be flush to the sides of the frame.

However, if that is done, the striker plate opening sticks out enough to make fastening a screw marginal at best.
Don't fuss about it. It's been that way for a very long time.

Doors are usually installed after the sheetrock is, so you can adjust the clamshell to the proper width, taking into consideration the thickness of the rock.